Detecting Stock Market Bubbles Based on the Cross‐Sectional Dispersion of Stock Prices
A statistical method is proposed for detecting stock market bubbles that occur when speculative funds concentrate on a small set of stocks. The bubble is defined by stock price diverging from the fundamentals. A firm’s financial standing is certainly a key fundamental attribute of that firm. The law of one price would dictate that firms of similar financial standing share similar fundamentals. We investigate the variation in market capitalization normalized by fundamentals that is estimated by Lasso regression of a firm’s financial standing. The market capitalization distribution has a substantially heavier upper tail during bubble periods, namely, the market capitalization gap opens up in a small subset of firms with similar fundamentals. This phenomenon suggests that speculative funds concentrate in this subset. We demonstrated that this phenomenon could have been used to detect the dot-com bubble of 1998-2000 in different stock exchanges.
It is common knowledge in macroeconomics that, as Federal Reserve Board Chairman Alan Greenspan said in 2002, ”...it is very difficult to identify a bubble until after the fact; that is, when its bursting confirms its existence.” In other words, before a bubble bursts, there is no way to establish whether the economy is in a bubble or not. In economics, a stock bubble is defined as a state in which speculative investment flows into a firm in excess of the firm’s fundamentals, so the market capitalization (= stock price × number of shares issued) becomes excessively high compared to the fundamentals. Unfortunately, it is exceedingly difficult to precisely measure a firm’s fundamentals and this has made it nearly impossible to detect a stock bubble by simply measuring the divergence between fundamentals and market capitalization [1–3]. On the other hand, we empirically know that market capitalization and PBR (= market capitalization / net assets) of some stocks increase during bubble periods [4–7]. However, they are also buoyed by rising fundamentals, so it is not always possible to figure out if increases can be attributed to an emerging bubble.